DECEPTIVE PRODUCTS AND COMPETITION IN SEARCH MARKETS

Transcription

1 DECEPTIVE PRODUCTS AND COMPETITION IN SEARCH MARKETS Tobias Gamp and Daniel Krähmer January 2017 Abstract We study a search market where firms have a choice between offering either efficient, high quality ( candid ) products or inefficient, low quality ( deceptive ) products which some ( naive ) consumers misperceive as of high quality. We derive an equilibrium in which both business models co-exist and show that as search frictions vanish, high quality goods are entirely driven out of the market. We show that market share and price dynamics can be non monotone in search frictions, and we argue that while policy interventions that reduce search frictions such as the standardization of price and package formats may harm welfare, a price floor regulation can improve welfare. Keywords: Deceptive product, Inferior product, Naivete, Consumer Search JEL Classification No.: D18, D21, D43, D83 We would like to thank Antonio Cabrales, Paul Heidhues, Botond Köszegi, Franceso Nava, Martin Peitz, Andrew Rhodes, Ran Spiegler and Tymon Tatur as well as seminar audiences in Mannheim and Düsseldorf for helpful comments and suggestions. Financial support by the Wissenschaftsförderung der Sparkassen-Finanzgruppe e.v. is gratefully acknowledged. University College London, Drayton House, 30 Gordon Street, London WC1H 0AX (United Kingdom); tobit.gamp@hotmail.de University of Bonn, Institute for Microeconomics, Adenauer Allee 24-42, D Bonn (Germany); kraehmer@hcm.uni-bonn.de 1

2 1 Introduction An important feature in many consumer markets is product complexity in the sense that fully understanding a product s features and assessing all consumption consequences requires technical, scientific, legal, or other expertise. This provides sellers of complex products with the opportunity to strategically frame and package their offers in ways that mislead consumers who lack this expertise. An important example are financial services whose understanding requires both financial literacy and an awareness of numerous future contingencies. Standard financial services such as mutual investment funds or credit cards are fraught with contract clauses and contingent fees hidden in fine print. As argued in Gabaix and Laibson (2006) and Armstrong and Vickers (2012), it is often difficult to make sense of such contract terms in traditional models of consumer behavior, as they generate enormous profits at the expense of few vulnerable consumers. 1 Another example are investment products composed of complex derivatives. Before the outbreak of the financial crisis, investment banks pushed the sale of seemingly top-rated, yet in truth toxic papers to ill-advised investors who were not aware of the risks they were exposed to. 2 Other examples of complex products comprise grocery products whose features (ingredients, health effects, origin, organic vs. non organic ), which are often prominently advertised, are difficult to ascertain for lay consumers, or consumer electronics where future usage costs are difficult to estimate. In this paper, we analyze a market for a complex product when consumers need to engage in costly search to detect the price and the fit of a product. 3 We capture the link between product complexity and deception by assuming that some ( naive ) consumers can be deceived about the true product quality. That is, firms have the choice of offering a candid product of high quality which all consumers recognize as such, or a deceptive product of low quality which naive consumers misperceive as a high quality product. 4 Candid products, while more costly to 1 For example, Armstrong and Vickers (2012) discuss insufficient fund charges that made up 30% of the total revenue generated by current accounts in the year 2006, however, were only incurred by 23% of all customers according to the Office of Fair Trading (2008). 2 As evidence of this, Deutsche Bank just recently agreed to pay a $3.1 billion penalty and to provide relief to American consumers valued at $4.1 billion in order to resolve a federal investigation of its sale of toxic mortgage backed securities. 3 As documented by Line and Wildenbeest (2015) for Medigap insurance, search is likely to be a key factor in markets for insurance and financial services. 4 Next to lack of expertise, there might be other, possibly complementary, reasons for consumer naivete which are 2

3 produce, are assumed to be socially efficient. As a result, in the benchmark without any naive consumers, competition ensures that firms only offer candid products. 5 In contrast, in this paper we will show that when some consumers are naive, there is an equilibrium which displays market segmentation where the deceptive and the candid business model co exist in the market. This equilibrium has some remarkable positive and normative comparative statics properties. As one of our main insights, we show that more intense competition in the form of lower search costs may have the detrimental effect that it increases the share of deceptive products in the market. Strikingly, in the limit, as search frictions get small, candid products are even entirely driven out of the market. 6 We will also discuss policy interventions that may, or may not, improve welfare. Among others, we will argue that policy measures that aim at facilitating price comparisons such as the imposition of standardized price or package format may be socially undesirable, and that a price floor regulation may improve welfare in our setting. Our finding that smaller search frictions may promote the share of deceptive products is consistent with the empirical evidence in Ellison and Ellison (2009) who report for the online market for memory modules that as a response to the better search technology (in particular for prices), firms began to bundle low-quality goods with unattractive contractual terms, like providing no warranty and charging a 20 % restocking fee on all returns. 7 We study market segmentation equilibria with the property that sophisticated consumers, who see through deception, never buy deceptive products but search until they find a suitable candid product. In contrast, naive consumer, who perceive all firms as homogeneous and fail to infer quality from price, purchase from the first firm they visit provided its price is in an acceptable range that makes continued search unviable. As we show, this implies that deceptive and candid widely accepted in the literature by now: limited attention, overconfidence in the own ability to assess products, overconfidence in the comprehensiveness of regulation, or vulnerability to persuasive sales techniques, to name a few. 5 In the absence of naive consumers, our model essentially corresponds to Wolinsky (1986) or Anderson and Renault (1999) where sellers compete in horizontally differentiated products, and consumers have to engage in costly search to observe price and product fit. 6 Away from the limit, on the other hand, market share dynamics as well as prices may be non-monotone in search costs. 7 Ellison and Ellison (2009) conclude that given the variety of terms we observed, it would seem unwise to purchase a product without reading the fine print. 3

4 firms charge similar prices in equilibrium, and since candid quality is more costly to produce, their product choice is driven by the trade-off between selling the candid product at a low mark up to all consumers and selling the deceptive product at a high mark-up to only naive consumers. Intuitively, market segmentation arises in equilibrium because naive consumers perceive all firms as homogeneous, and so their demand is inelastic as in Diamond (1971). Hence, deceptive firms can charge positive mark-ups ensuring strictly positive profits. In contrast, since candid firms compete for sophisticated consumers who compare prices, the mark-up of a candid firm depends on the number of candid competitors in the market. Therefore, for given search costs, one business model cannot exist alone, because if there are predominantly deceptive firms in the market, then offering a candid product gets relatively more profitable, as it attracts large demand from sophisticated consumers who are divided up between very few candid firms. Reversely, if there are predominantly candid firms in the market, deception can be seen as a way to avoid the fierce competition in the candid segment. Our first comparative statics result states that in the limit, as search costs get small, candid firms are entirely driven out of the market. Thus, if only a small fraction of consumers is vulnerable to deception, intense competition in the form of small search costs has the striking consequence that the market will supply only deceptive quality. The basic intuition is that, as search costs get small, sophisticated consumers can compare firms essentially for free. This intensifies competition in the candid segment and eliminates a candid firm s mark-up and profit, ultimately leading all firms to adopt the deceptive business model which guarantees positive profits. 8 While our limit result suggests that the number of candid firms in the market is increasing in search costs, this holds only under additional conditions. In fact, we show by an example that the fraction of candid firms may also decline in search costs. When this is the case, the price a candid firm charges may actually decrease with search costs. Similarly to standard search models, as search costs increase, sophisticated consumers search less, allowing candid firms, all else equal, to increase their price. In our framework, there is, however, an additional and novel indirect effect because the number of candid firms is endogenous. As we show, if the number of candid 8 As we explain in the main text in detail, this intuition is somewhat incomplete because what matters for sophisticated consumers is not nominal, but effective search costs, that is, the costs it takes to find not any, but a candid firm. As we show, effective search costs are monotone in nominal search costs and, in fact, go to zero if nominal search costs do. 4

5 firms drops, a single candid firm s demand gets more elastic, pushing its price down. Hence, if the fraction of candid firms decreases in search costs, this force works against the familiar effect that prices increase as consumers search less. 9 Our comparative statics results suggest that changes in search costs may have non standard welfare effects in our setting. In fact, we show that total welfare may increase in search costs. This is the case if the share of candid firms increases in search costs and the efficiency gains from a candid product are sufficiently large. Since prices are a wash from the perspective of total welfare, efficiency gains may then outweigh the higher search costs consumers incur. The ensuing welfare gains will, however, be unequally distributed among the market participants: Sophisticated consumers lose out because they are harmed by higher prices and higher search costs, whereas firms gain, and the effect on naive consumer welfare depends on whether the average quality increase offsets the price increase. In the case in which welfare increases in search costs, policy interventions that aim at reducing search costs are undesirable. This may include policies that facilitate the comparability of products, such as requiring firms to use standardized price, package, and product information formats, or the promotion of online marketplaces that facilitate the exchange of price information. Another policy measure that is often discussed in the context of complex products are information and education campaigns that create consumer awareness (such as promoting financial literacy in the context of financial service markets). In our framework, this amounts to reducing consumer naivete. As we show, reducing the number of naive consumers is beneficial for both naive and sophisticated consumer welfare. The reason is that with a shrinking naive customer base, fewer firms adopt the deceptive business model. This not only reduces the effective search costs sophisticated consumer incur on average, but also creates more price pressure in the candid segment. In this sense, naive consumers exert a negative externality on sophisticated consumers in our framework. 10 In our setting, price competition becomes dysfunctional because naive consumers constitute 9 We also study the effects of changes in the number of naive consumers on market shares and prices. While the directions of these effects are as expected (the share of candid firms and prices increase in the number of naive consumers), they are surprisingly non straightforward to establish. 10 This is in contrast to models where firms exploit naive consumers and use the proceeds to compete for sophisticated consumers (see, e.g., Gabaix and Laibson (2006), Armstrong and Vickers (2012).) 5

6 a safe profit haven for firms: the tighter the margins in the candid segment, the higher the incentives to adopt the deceptive business model which guarantees positive profits. This suggests that impeding price competition by imposing a price floor might be beneficial in our framework. To address this point, we consider the effect of an exogenously imposed (marginal) price increase relative to the equilibrium price. As we show, this always improves total welfare because it makes offering candid products more profitable. Despite the price increase, a price floor regulation may even increase consumer welfare if the ensuing increase in the number of candid firms is sufficiently large. Our paper is related to a literature in behavioral industrial organization which studies how firms (can) exploit boundedly rational consumers. Most closely related are papers which study markets where firms offer goods with (unavoidable) future add-on services which naive consumers fail to anticipate. We contribute to this literature by adding consumer search to the picture, allowing entirely novel dimensions of comparative statics, in particular with respect to search frictions. More specifically, in Gabaix and Laibson (2006), Armstrong and Vickers (2012) and Heidhues et al. (2017) deception occurs when firms engage in hidden add on pricing, possibly leaving naive consumers with utility below their outside option. While in our framework, a deceptive good can be interpreted as a good with hidden unavoidable add-on costs, firms cannot price or disclose (unshroud) the add-on. 11 In the latter respect, our model is similar to Armstrong and Vickers (2012) which focuses on add-on pricing alone and finds that all firms generically either engage in or abstain from deceptive add-on pricing in equilibrium. In contrast, a key point of our paper is that the deceptive and non-deceptive business model co-exist. Our finding that sophisticated consumers are harmed by the presence of naive ones stands in contrast to the opposite finding in Gabaix and Laibson (2006) and Armstrong and Vickers (2012), but is consistent with Heidhues et al. (2017) where deceptive equilibria exist only if there are enough naive consumers in which case sophisticates abstain from the market. In contrast, in our setting, sophisticates still consume, but due to the presence of naive consumers, have to search longer and pay higher prices. A final, rather striking, difference between Heidhues et al. (2017) s and us is that the existence of an (exogenous) price floor is the root cause for equilibrium deception in their work, whereas 11 In an extension to our basic model, we discuss the possibility that firms can unshroud, that is, turn naive into sophisticated consumers, and we show that in equilibrium neither deceptive nor candid firms have incentives to do so. 6

7 in our setting, a price floor regulation can mitigate deception. A closely related paper is also Piccione and Spiegler (2012) whose analysis, like ours, implies that policy interventions that aim at facilitating the comparability of products, for example by mandating standardized price formats, can turn out to harm consumer welfare. The underlying reason is, however, rather different. In Piccione and Spiegler (2012), firms choose price and pricing formats which determine whether consumers can compare prices across firms. Firms face a trade-off between maximizing sales volume by combining low prices with easily comparable formats and maximizing mark ups by combining high prices with onerously comparable formats. Piccione and Spiegler (2012) identify conditions under which ( local ) interventions that make relatively easily comparable formats even more easily comparable may backfire because the intervention makes the strategy which combines high prices with onerous comparability more profitable at the margin. As a result, prices will increase on average. If, on the other hand, the intervention is global and makes all formats more easily comparable, then Piccione and Spiegler (2012) show that the intervention is desirable. In contrast, in our model, prices may drop if they become more easily comparable, and what makes the intervention undesirable is that the quality in the market deteriorates, suggesting competing testable predictions. Also, in our framework, interventions that ease comparability (i.e., reduction in search costs) are global by definition. Finally, the underlying consumer bias is different. Whereas consumers in Piccione and Spiegler (2012) have difficulties in comparing prices, they have difficulties to assess a product s quality in our setting, suggesting different domains of applicability. 12 Moreover, our paper contributes to the industrial organization literature on consumer search by integrating naive consumers and seller deception into the seminal papers by Wolinsky (1986) and Anderson and Renault (1999). Our result that prices may increase as search costs fall has appeared before in the literature but for different reasons, among others in Janssen and Moraga-González (2004), Armstrong and Zhou (2011), Janssen and Shelgia (2015), and Moraga- 12 To the extent that seemingly pro competitive interventions may backfire, our paper is also related to Varian (1980) s model of sales where firms set prices so as to trade off attracting consumers who compare prices across firms and reaping loyal customers who do not compare prices. An intervention which leads to a higher number of competitors may backfire because it makes reaping loyal consumer relatively more profitable, entailing an average price increase. Also in Vickers et al. (2009), the seemingly consumer-friendly introduction of a price cap may actually be harmful such that consumers pay higher prices on average, as it reduces their incentives to search. 7

8 González et al. (2017). 13 In our case, it originates in the fact that the share of candid firms is endogenous which affects both effective search costs and the composition of demand for an individual firm. Somewhat similarly, in Moraga-González et al. (2017), lower search costs alter the composition of demand, but in their case, this is due to the market entry of less versed consumers whose demand is less elastic. The connection between the share of candid firms and effective search costs is somewhat reminiscent of Eliaz and Spiegler (2011) where a search engine operator may encourage low-relevance advertisers to enter the search pool in order to raise effective search costs and hence advertisers profits with the goal to extract some of these profits with fees. 14 The theme that consumers are unaware of what kind of products they purchase also appears in Gamp (2016) who considers consumer who trade off the risks of a bad buy with the savings on search costs, so that it is a rational consumer s decision to remain uninformed. In contrast to the current paper, Gamp (2016) focuses on the pricing and obfuscation strategies of firms under market conditions rather than on their product choice. This paper is organized as follows. The next section introduces the model. Section 3 derives equilibrium conditions. Section 4 and 5 perform comparative statics, and section 6 discusses policy implications. Section 7 discusses extensions, and section 8 concludes. All proofs are in the appendix. 2 Model We consider a search market with a unit mass of firms indexed by k [0, 1] and a unit mass of consumers indexed by i [0, 1]. Each consumer seeks to purchase at most one good. Goods are differentiated with a horizontal and a vertical component. Formally, consumer i s utility from purchasing the good offered by firm k is equal to u ik = q k + µθ ik p k, (1) where q k is the quality offered and p k is the price chosen by firm k. The term µθ ik represents a consumer-firm specific match-value, where µ > 0 is a measure of the importance of product fit relative to quality, or of the degree of (non-)substitutability of products. It is common knowledge that for all i, k, the associated random variable θ ik is distributed on the support [θ, θ] with 13 See also Cachon et al. (2008) and Choi et al. (2016). 14 Similarly, in Ireland (2007) sellers posit multiple prices to reduce the effectiveness of consumer price search. 8

9 (sufficiently smooth) cumulative density function F and mean zero (hence θ < 0), independent and identical across consumers and firms. We assume that the corresponding probability density function f is log-concave with f (θ) > 0 which implies that F has an increasing and unbounded hazard rate h(θ) = f (θ) 1 F(θ). (2) The objective of our analysis is to study market outcomes when some consumers can be deceived about the true quality of a product. To capture this, we assume that firms can offer either a candid good of high quality q or a deceptive good of low quality q < q. The low quality product, however, is disguised (due to packaging, fine print, sales techniques,... ) so that some consumers misperceive it as a high quality product. The (true) quality of a product determines its production costs with c(q) being the marginal costs for producing a good with quality q. Let c = c(q) and c = c(q), with c < c. Moreover, let c = c c and q = q q. To make the problem interesting, we assume that the candid good is socially efficient, q > c, (3) and that consumers, net of prices, prefer a candid over a deceptive product even if the former displays the worst and the latter the best product fit: q > µ (θ θ). (4) To purchase a product from a firm, a consumer has to visit it which entails a (search) cost. A consumer may visit several firms, one at a time and in a random order so as to extend his choice set of products. Prior to visiting a firm, a consumer is uninformed about its price p k and its product s characteristics (q k, θ ik ). To capture formally that some consumers are susceptible to deception and misperceive a low quality for a high quality product, we assume that there is a fraction ν N of naive consumers. Upon visiting a firm k, a naive consumer observes the price p k, but does not observe the product s characteristics (q k, θ ik ). Instead, he (incorrectly) believes the quality of all products to be high (equal to q) and the expected match-value to be zero The assumption that naive consumers do not observe a product s characteristics effectively means that naive consumers lack the ability to assess both a product s quality and whether it is suited to their needs. The assumption that naive consumers have correct (rather than inflated) beliefs about match-values is for simplicity and insignificant for our results. In Section 7, we discuss the case in which naive consumers do observe the match-value and show that our main result, that candid products are driven out of the market as search costs get small, still holds. 9

10 In contrast, a fraction ν S of sophisticated consumers, upon visiting a firm, observes prices and product characteristics and holds correct beliefs. In particular, they recognize deceptive products as what they are. The sequence of events is as follows. At the outset, firms simultaneously, independently, and once and for all set q k and p k. Consumers then search until they purchase a product. That is, at any point in time, they decide whether to visit an additional firm at random at search costs s > 0, or to buy a product from a previously visited firm (and afterwards leave the market). 16 Thus, a strategy for a firm is a quality-price combination, and a strategy for consumers is a search rule that specifies whether to end or continue search contingent on the past search history. We adopt a concept of equilibrium which is essentially Perfect Bayesian equilibrium except that naive consumers have incorrect beliefs. That is, we define an equilibrium as a strategy profile where firms and all consumers adopt optimal strategies given their beliefs about the other players strategies. The beliefs of firms and sophisticated consumers are consistent with the other players strategies, while the beliefs of naive consumers are misspecified as follows: they believe that any firm chooses the high quality q and displays the pricing behavior of a firm that indeed selects high quality. 17 In the first step of our analysis, we establish necessary and sufficient conditions for the existence of an equilibrium which displays a segmentation of the market in a candid and a deceptive segment: a fraction λ of candid firms targets sophisticated consumers by offering quality q at a common price p, and a fraction 1 λ of deceptive firms targets naive consumers by offering quality q at the price p. Sophisticated consumers search until they find a suitable candid product, while, in contrast, naive consumers buy from the first firm they visit. Definition 1 A triple (λ, p, p ) (0, 1) 2 is a segmented market equilibrium outcome (with search) if there is an equilibrium in which 16 We implicitly assume that consumers have no interest in leaving the market without purchasing a product, hence participation constraints are met. 17 More precisely, a strategy of a firm is a probability distribution over qualities and prices, and a naive consumer believes that any firm adopts high quality and chooses prices according to the (correct) conditional distribution of prices conditional on high quality. If this conditional distribution is not defined because no firm chooses high quality (which will not occur in our analysis below though) then we allow for arbitrary beliefs about prices by naive consumers. 10

11 a fraction λ of firms offers a candid good with q k = q and p k = p ; a fraction 1 λ of firms offers a deceptive good with q k = q and p k = p ; sophisticated consumers never buy a deceptive good; naive consumers buy candid and deceptive goods. Note that the definition requires the share λ of candid firms to be interior. We refer to an equilibrium which supports a segmented market outcome as a segmented market equilibrium. 3 Conditions for market segmentation In this section, we establish necessary and sufficient conditions for the existence of a segmented market equilibrium. We begin by deriving sophisticated consumers optimal search rule if they expect a segmented market equilibrium outcome (λ, p, p). Sophisticated consumer search Because a searching consumer samples the next firm at random from the pool of all firms, a sophisticated consumer s optimal strategy is characterized by a reservation utility Û S which is the smallest level of utility that a consumer needs to obtain from purchasing a good so that he stops to search. As is shown by McCall (1970), the reservation utility leaves a consumer indifferent between purchasing at the current firm and visiting a single additional firm. In a segmented market (λ, p, p), a sophisticated consumer expects to encounter a candid firm with probability λ and a deceptive firm with probability 1 λ. Under the hypothesis that a sophisticated consumer does not buy a deceptive product, the reservation utility is therefore given recursively as θ Û S = λ max{q + µθ p, Û S } df(θ) + (1 λ)û S s. (5) θ A sophisticated consumer does indeed not buy a deceptive product for any match-value if: Û S q + µθ p. (6) It will often be more convenient to work with reservation match-values rather than reservation values. The reservation match-value is defined as the match-value ˆθ at which a sophisticated consumer is indifferent between buying a candid product with this match-value offered at p and continuing search: q + µ ˆθ p = Û S, (7) 11

12 and condition (6), that a sophisticated consumer does not to buy at a deceptive firm, becomes equivalent to q + µ ˆθ p q + µθ p. (8) To write condition (5) more succinctly, define the function g : by g(z) θ so that with (7) and (9), (5) can be written as θ max{θ z, 0} df(θ), (9) g( ˆθ) = s λµ. (10) As we show in Lemma A.1 in the appendix, the function g is strictly decreasing on (, θ] with g( ) = and g(θ) = 0. Therefore, equation (10) has a unique solution. Naive consumer search Also the naive consumer s optimal search rule is characterized by a reservation utility. In a segmented market equilibrium, a naive consumer (wrongly) expects all firms, including any random next firm, to offer a high quality product at price p. Because a naive consumer cannot observe match-values, his reservation utility is therefore given recursively as Û N = max{q + µ(θ) p, Û N } s, (11) so that because (θ) = 0, we have Û N = q p s. (12) Notice that for a naive consumer to indeed buy candid and deceptive products, both a candid and deceptive product must supply more (perceived) utility than Û N. That is, q p Û N, and q p Û N, which, by (12), boils down to p p + s. (13) This, in particular, implies that in a segmented market equilibrium, a naive consumer actually buys from the first firm he visits. Demand and firm profits To determine firms optimal pricing strategies, we now derive demand and profits in the two 12

13 segments. The following lemma states the profits of a given firm k that charges price p k taking as given that all other firms and consumers adopt the strategy as specified in a (candidate) equilibrium with outcome (λ, p, p). To state the lemma, we define for a given p and ˆθ: 1 F Π(p, q, c) = ν N (p c) + νs λ (p p) (q q) ˆθ + µ 1 F( ˆθ) (p c). (14) Lemma 1 In a segmented market equilibrium with outcome (λ, p, p), the profit of a firm that sets quality q k and price p k is given by Π(p k, q k, c(q k )) i f p k p + s; π(q k, p k ) = Π(p k, q k, c(q k )) ν N (p k c(q k )) i f p k > p + s, (15) and equilibrium profits are given by π(q, p) = ν N (p c) and π(q, p) = (ν N + νs ) (p c). (16) λ To see what is behind the lemma, note first that the profit of a firm is given as the product of (a) the mass of consumers who visit the firm in its lifetime, (b) the probability that a visitor actually purchases the good, and (c) the firm s mark-up (p k c). In a segmented market equilibrium, (a) comes about as follows. First, recall that all naive consumers buy in the first period and leave the market afterwards. Thus, the mass of naive consumers who visit a given firm in its lifetime is simply equal to ν N. Second, the mass of sophisticated consumers who visit a given firm in period t is equal to the mass of sophisticated consumers who are still in the market in this period. In a segmented market equilibrium, a sophisticated consumer leaves the market if he is matched with a candid firm that displays a match-value exceeding the consumer s reservation match-value, occurring with probability λ(1 F( ˆθ)). Thus, the mass of sophisticated consumers who visit a given firm in period t is equal to the mass of sophisticated consumers who have not left the market prior to t which is ν S [1 λ(1 F( ˆθ))] t. Hence, the (expected) mass of sophisticated consumers who visit a given firm in its lifetime is equal to κ = ν S [1 λ(1 F( ˆθ))] t ν S =. (17) λ(1 F( ˆθ)) t=0 Next, we determine (b), the probability that a visitor actually purchases at the firm. If a sophisticated consumer i visits a firm k with quality q k and price p k, he purchases if firm k supplies 13

14 him with a higher utility than the reservation utility Û S. By (5) and (7), this is the case if q k + µθ ik p k q + µ ˆθ p θ ik ˆθ + (p k p) (q k q). (18) µ Moreover, all naive consumers who visit firm k buy as long as p k p +s. A firm k that sets q k and p k p + s therefore earns the profit π(q k, p k ) = ν N (p k c(q k )) + κ 1 F ˆθ + (p k p) (q k q) (p k c(q k )). (19) µ Inserting (17) delivers (15). Finally, if a firm deviates to a price p k > p + s, it loses the profits ν N (p k c(q k )) it would otherwise make from naive consumers. The expressions for equilibrium profits in (16) follow immediately by inserting equilibrium prices p and p and the respective qualities q and q in (15), taking into account that p p + s by (13). Equilibrium Our next step is to characterize segmented market equilibrium outcomes formally. We will focus on equilibria with actual consumer search and rule out the less interesting case in which all consumers, including sophisticated ones, purchase from the first firm they visit, irrespective of match-values. In other words, we restrict attention to equilibria in which sophisticated consumers strictly prefer continuing search to purchasing a product at p which exhibits the smallest match-value possible. That is, the equilibrium reservation match-value ˆθ is in the interior of the support of match-values. From now on, when we refer to equilibrium, we mean such an equilibrium in which actual search takes place. From a technical point of view, the restriction to equilibria with interior reservation matchvalues facilitates tractability, as it allows us to characterize optimal firm behavior by first order conditions. 18 In the next lemma, we provide a system of equations whose solution corresponds to a segmented market equilibrium outcome. To ensure that first order conditions are also sufficient for 18 In principle, there may be equilibria with ˆθ = θ in which sophisticated consumers buy with probability 1 at the first firm they visit. Intuitively, if sophisticated strictly prefer to purchase at the first firm, then a candid firm s demand would be (locally) inelastic so that it would prefer to raise its price. In these equilibria, however, the fraction of candid firms adjusts such that sophisticated consumers are exactly indifferent between continuing and discontinuing search if they find a product which displays the worst match-value ( ˆθ = θ). A candid firm s profit function then has a kink at the equilibrium price so that its pricing behavior cannot be characterized by first order conditions. 14

15 optimality, we impose the following regularity condition: Note that the condition always holds with increasing density. 19 f (θ) f (θ) νs f (θ). (20) νn Lemma 2 Suppose condition (20) holds. Then (λ, p, p ) is a segmented market equilibrium outcome if and only if there is ˆθ (θ, θ) and λ (0, 1) so that: ν N + νs λ g( ˆθ ) = s λ µ, (21) νn p 1 + λ ν c = µ S h( ˆθ ), (22) p c = p c + s + c, (23) (p c) = ν N (p c). (24) To understand Lemma 2, notice first that (21) is the same condition as (10). Second, (22) corresponds to the first order condition for p to be profit maximizing for a candid firm, expressed in terms of the mark-up p c. Because of (20), the first order condition is also sufficient. Third, condition (23) reflects that p is profit maximizing for a deceptive firm and says that a deceptive firm s equilibrium mark-up equals the mark-up of a candid firm plus an additional mark-up of s + c. In light of (22), this means that the profit maximizing price of a deceptive firm is p = p + s. The reason is that by expression (15), a deceptive firm s demand is inelastic up to the price p + s. Importantly, the mark-up of a deceptive firm is hence bounded from below by c. Fourth, condition (24) says that candid and deceptive firms make the same profits. This has to hold in equilibrium, because otherwise firms in the less profitable segment would want to move to the more profitable one. Thus, the profit that a firm earns by selling deceptive products at a 19 It is standard in the search literature to impose sufficient conditions similar to (20) which ensure that first order conditions are sufficient for profit maximization. In the absence of naive consumers (ν N = 0), our model is akin to Wolinsky (1986) who only requires that the hazard rate of F be increasing (see the footnote on page 504). This is consistent with (20), because if ν N is sufficiently small, (20) is satisfied under the mild assumption f (θ) > 0, and because our assumption of log-concavity of f implies an increasing hazard rate. A condition similar to (20) is also adopted by Anderson and Renault (1999). 15

16 higher mark-up to only naive consumers is equal to the profit that a firm earns by selling candid products at a lower mark-up to naive and sophisticated consumers. From now on, we impose condition (20) as a general assumption without further mention. Equilibrium existence and uniqueness We now ask when an equilibrium exists. At a fundamental level, candid and deceptive firms may co-exist in equilibrium if, as we vary the size of a segment exogenously, then as one segment gets large, profits in the larger segment fall below the profits in the smaller segment, creating incentives for firms in the larger segment to adopt the business model from the smaller segment. Intuitively, two forces drive profit differences. On the one hand, the smaller the candid segment, the larger are a candid firm s profits, because the demand of sophisticated consumers gets divided up between a smaller mass of candid firms. Thus, the demand of a candid firm in fact grows without bound as the share of candid firms gets small. On the other hand, if the candid segment is rather large, more firms compete for sophisticated consumers, pushing down a candid firm s profits. For market segmentation to occur in equilibrium, this effect has to be sufficiently strong so that profits of candid firms are pushed below that of deceptive firms if the candid segment is large. We now make these considerations more precise. Treating the share of candid firms λ as exogenous for the moment, the equilibrium conditions (21) and (22) pin down candid prices as function of λ as p (λ) c µ 1 + λ νn ν S h(g 1 ( s (25) λµ )), where g 1 is the inverse of g as defined in Lemma A.1 in the appendix. Inserting this, together with (23), in firm profits, we obtain the difference between a candid and a deceptive firm s profits as (λ) π π = νs λ p (λ) c ν N (s + c), (26) The equal profit requirement (24) then amounts to the condition (λ ) = 0. Hence, a segmented market equilibrium exists (and is unique) if the equation (λ) = 0 has a (unique) solution λ (0, 1) so that ˆθ (θ, θ). As shown in Lemma A.1 in the appendix, ˆθ is indeed in (θ, θ) if and only if λ > s µθ. The next proposition summarizes. 16

17 Proposition 1 There is a (unique) segmented market equilibrium outcome (λ, p, p ) if and only if (λ) = 0 has a (unique) solution λ with s µθ < λ < 1. The solution λ is the equilibrium share of candid firms, and equilibrium prices are pinned down by (22-23). 20 The next proposition confirms formally the intuition that offering a candid product becomes less attractive the more firms do so. This then allows us to show that a unique segmented market equilibrium outcome always exists if search costs are sufficiently small. Proposition 2 (i) is strictly decreasing in λ. (ii) For sufficiently small search costs, there is a unique segmented market equilibrium outcome. Part (i) follows by a calculation, exploiting the fact that the hazard rate is increasing. Part (ii) employs an intermediate value argument to show that (λ) = 0 has a unique solution in the range ( s µθ, 1) provided search costs s are sufficiently small. Consequently, a unique segmented market equilibrium outcome exists by Proposition 1. To understand more intuitively the role of search costs for the co-existence of candid and deceptive firms in equilibrium, recall from above the two forces behind profit differences in the candid and deceptive segment. On the one hand, if (almost) all firms are candid, and search costs get close to zero, the mark-up for candid firms, while staying positive as long as search costs are positive, gets arbitrarily close to zero, 21 whereas the mark-up for deceptive firms is bounded from below by c. Therefore, if (almost) all firms are candid, there is a level of search costs below which candid firms earn lower profits than deceptive firms. On the other hand, recall that demand for candid firms increases monotonically without bound as the share of candid firms shrinks. Hence, even if search costs and hence mark-ups are tiny, profits in the candid segment are very large if (almost) no firm is candid. As a consequence, there is an intermediate share of candid firms where the profits in the two segments equalize. In what follows, we assume that search costs are such that a unique segmented market equilibrium exists. This allows us to study the comparative statics of segmented market equilibrium 20 Note that a segmented market equilibrium can only exist if s µθ < 1, which is a standard condition (for consumer search to take place) in the search literature (see e.g. Wolinsky (1986) and Anderson and Renault (1999)). We implicitly impose s µθ < 1 below by imposing the stronger condition (54). 21 Formally, as s/λ 0, equation (21) and the definition of g imply that ˆθ converges to θ. It follows that the mark-up p c given by (22) converges to zero because the hazard rate is unbounded. 17

18 outcomes. To do so, we will abuse notation and denote by p, p and ˆθ both the equilibrium outcomes which depend only on exogenous parameters, as well as the best reply functions p ( ), p ( ) and ˆθ ( ) which are pinned down by (21-23) as functions of λ when treated as an independent variable such as in equation (25). In particular, we use total derivatives to indicate changes of equilibrium outcomes, and partial derivatives to indicate changes of the best reply, taking λ as given Effects of changes in search costs In this section, we investigate how changes in the intensity of competition, as captured by changes in search costs, affect market outcomes. We begin by considering how competition affects the size of the two segments and hence the quality provision in the market. Market segmentation Our first result says that as search costs vanish, candid firms are entirely driven out of the market. Proposition 3 As search costs vanish, candid firms are entirely driven out of the market: lim s 0 λ = 0. In other words, when only some consumers are vulnerable to deception, then intense competition has the striking consequence that the market will supply only deceptive quality. In a nutshell, the intuition is that vanishing search costs allow sophisticated consumers to compare firms essentially for free. This intensifies competition in the candid segment, thus eliminating candid firms mark-ups and profits, ultimately leading all firms to adopt the deceptive business model which guarantees positive profits. This intuition hides the subtlety that what matters for sophisticated consumers is not nominal search costs, but the expected search costs to encounter a candid firm. If nominal search costs are one dollar, and among 100 firms there is only a single candid firm, a sophisticated consumer has to spend on average 100 dollars to find a candid firm. Thus, the effective search costs that a sophisticated consumer faces in equilibrium are the expected search costs σ s λ. (27) 22 For example, dp /ds is the change of the candid equilibrium price with respect to s, whereas p / s is the change of the candid equilibrium price with respect to s when λ does not adjust to the change in s. Therefore: dp /ds = p / s + p / λ dλ /ds. 18

19 Observe that a candid firm s mark up goes to zero as search costs vanish only if also effective search costs go to zero, because only then a sophisticated consumer can inspect an additional candid firm essentially for free, inducing firms to compete intensely with each other. (Formally, this is shown in footnote 21.) With this in mind, the intuition behind Proposition 3 can now be made more precise. If the share of candid firms λ did not converge to zero, then effective search costs s/λ would tend to zero as s approaches zero, and candid firms mark ups would erode. Because firms make strictly positive profits in equilibrium, the erosion of mark ups must be offset by an unbounded increase in the demand of a candid firm which, in turn, requires that the share of candid firms shrinks to zero (recall that in equilibrium a candid firm attracts the demand ν S /λ from sophisticated consumers) a contradiction. 23 Proposition 3 shows that very stiff competition where search costs are virtually eliminated is detrimental for the quality provision in the market. We now ask whether it is true in general that lowering search costs, but not all the way to zero, has the detrimental effect that it decreases the share of candid firms in the market. The next result establishes sufficient conditions for this to be the case. Below, we will, however, identify opposite cases where lower search costs increase the number of candid firms. Thus, the effect of search costs on quality provision is, in general, ambiguous. Proposition 4 (i) If search costs are sufficiently small, then the share of candid firms increases in s. (ii) The share of candid firms increases in s if h ( ˆθ )/h( ˆθ ) µ/ c. (iii) The share of candid firms strictly increases in s if f ( ˆθ ) 0. In order to illuminate the intuition, we illustrate the economic forces that drive the evolution of market segments as search costs change. If profits in the candid segment increase by more than in the deceptive segment, then the candid business model becomes more attractive, and the 23 This reasoning also implies that effective search costs vanish as search costs get small: lim s 0 σ = 0. In this sense, our model displays the property that in the zero search cost limit, the market is frictionless. Intuitively, suppose that effective search costs did not vanish as search costs tend to zero, this would imply that candid firms would charge strictly positive mark ups (at least along some sequence of search costs tending to zero). But as a candid firm s demand grows without bound as search costs get small, because λ vanishes, its profits would hence explode which is impossible in equilibrium. 19

20 candid segment grows as an equilibrium response (and vice versa). Recall that the equilibrium price of a deceptive and a candid firm differ by search costs: p = p +s. Therefore, if search costs increase by one dollar, a deceptive firm can enforce even larger mark-ups to naive consumers, and its price increases by one dollar more than the price of a candid firm. Now, deceptive and candid firms have the same number ν N of naive customers, while a candid firm serves an additional ν S /λ sophisticated consumers in equilibrium. As search costs increase marginally, a deceptive firm thus earns one marginal dollar more than a candid firm per naive customer, while candid firm earns p / s marginal dollars more from any of its sophisticated consumers. Hence, as search costs rise, the difference between the change in candid and deceptive profits is s = νs λ p s νn. (28) Observe that the partial price effect p / s is always non-negative as in Wolinsky (1986). 24 As a consequence, (28) is positive if either λ is small or p / s is large. We can now provide the intuition behind Proposition 4. As for part (i), by Proposition 3, the share of candid firms is tiny if search costs are tiny, implying huge sophisticated demand per candid firm, and expression (28) is consequently positive. As an equilibrium response, the candid segment increases as s increases. Parts (ii) and (iii) on the other hand state sufficient conditions for the marginal price change p / s to be large. To see this, recall from (25) that p / s is related to the steepness of the hazard rate because the hazard rate indicates the percentage increase in the mass of sophisticated consumers who will stop to search and buy the firm s product if it marginally decreases its price. Thus, the larger the hazard rate, the larger is a candid firm s demand elasticity, and the smaller is the equilibrium price. Therefore, the price a candid firm charges increases sharply in s if the hazard rate decreases sharply, rendering expression (28) positive. While (ii) and (iii) are stated in terms of the endogenous cutoff ˆθ, we can turn them into primitive conditions by requiring them to hold for all θ. For example, (iii) is satisfied for the uniform distribution. The previous considerations suggest that if the change in the hazard rate is sufficiently small, the marginal price effect p / s might be so small that (28) becomes negative. At such a point, 24 This is the case, because if the share of candid firms is kept fix, an increase in search costs induces sophisticated consumers to search less. Thus, the critical match-value ˆθ goes down, making the demand by sophisticated consumers less elastic (as the hazard rate is increasing) which allows firms to increase prices. 20

21 the share of candid firms would decrease in s. We now give a parameterized example in order to illustrate that this may indeed be the case. The example takes the exponential distribution, which displays a constant hazard rate, and truncates it so as to adapt it to our setting with bounded support. (The calculations behind the example are provided in Appendix B.) Example Let [θ, θ] = [ 1, 1], and define e (θ+1) θ < 0 f E (θ) = e 1 θ 0. (29) Let f = f E. Then there is an open set of parameters s, µ, q, q, c, c, ν N so that a segmented market equilibrium exists with ˆθ < 0 and λ = νs ν µ N s + c µ. (30) The example has the property that the equilibrium match-value ˆθ is below zero, and that, at ˆθ, the distribution coincides with an exponential distribution. Thus, the demand elasticity is constant, and the change of the demand elasticity is zero. As can be seen immediately from (22), this implies that p / s = 0. In other words, as search costs increase, all else equal, candid profits do not change while deceptive profits increase because deceptive prices increase with s. As a result, the number of candid firms must drop as s increases. Price effects We now study how equilibrium prices evolve as search costs change. We focus on candid prices, as deceptive prices only differ by s. The key observation to understand price dynamics is that candid prices depend on search costs s only through effective search costs σ = s/λ. Indeed, by (25): p c = µ 1 + λ νn ν S h(g 1 (σ/µ). (31) To understand the comparatives statics of prices, we consequently begin with the comparative statics of effective search costs: Lemma 3 Equilibrium effective search costs are increasing in s: dσ /ds 0. To see the intuition behind the lemma, recall that per naive consumer, a deceptive firm earns one dollar more than a candid firm as search costs increase by one dollar. Now, if effective search costs 21